1. The problem statement, all variables and given/known data To clarify- this isn't a homework problem; its something that's stated as a corollary in my notes (as in the proof is supposed to be obvious) and I haven't yet managed to prove it- I'm probably just missing something! Would appreciate a hint or a link to where I might find the proof. Let X be a normed vector space, t [itex]\in[/itex] X such that for all g [itex]\in[/itex] X', g(t) = 0. Then t = 0. 2. Relevant equations Hahn-Banach Theorem (stated on my course as:) Let M be a subspace of a normed vector space X. Let f [itex]\in[/itex] M' . Then there exists g [itex]\in[/itex] X' such that the norm of f (wrt M') is equal to the norm of g (wrt X'), and g is equal to f on M. 3. The attempt at a solution Just a bit confused- this is equivalent to, the only point all linear functionals can vanish at is zero. Presumably I want to define some linear subspace to then use but the only one that jumps out at me is span(t) which then doesn't seem to give me anything. Any hints?